关于模糊粗糙集的一个注记

A note on the fuzzy rough sets

指出文献[6]中定义的模糊粗糙集的补集不再是模糊粗糙集.为了克服原定义中的缺陷,给出了关于模糊粗糙集的新的补集定义,讨论了相应的运算性质.同时还证明:模糊粗糙集其实就是定义在F格L上的L-模糊集.

[6] in the bibliography has given the concept of fuzzy rough sets as the combination of fuzzy sets and rough sets. But it is pointed out in our paper that the complement set of the fuzzy rough set in [6] does not satisfy the condition of fuzzy rough set, i.e, the definition in [6] can not guarantee the closeness of FR（X） for the complement operation. In order to overcome this shortcoming, we have given a new definition of the complement set. Moreover, we have proved that a fuzzy rough set is a L-fuzzy set in the ordinary sense.